Linac Basics

 

A LINear ACcelerator or LINAC, is a particle accelerator which accelerates charged particles - electrons, protons or heavy ions - in a straight line.

Charged particles enter on the left and are accelerated towards the first drift tube by an electric field. Once inside the drift tube, they are shielded from the field and drift through at a constant velocity. When they arrive at the next gap, the field accelerates them again until they reach the next drift tube. This continues, with the particles picking up more and more energy in each gap, until they shoot out of the accelerator on the right.

The drift tubes are necessary because an alternating field is used and without them, the field would alternately accelerate and decelerate the particles. The drift tubes shield the particles for the length of time that the field would be decelerating

 

The linear accelerator, or linac, is the electromagnetic catapult that brings electrons from a standing start to relativistic velocity--a velocity near the speed of light. Here is a photo of the FNRF linac.

 

 

The linac is ~2.5 meters long--not a great distance in which to get even an electron from zero to almost 300,000 kilometers per second. How is it possible? Here's a simplified drawing that shows how a linear accelerator works:

 

 

 

The major parts of a linear accelerator are:

• The electron gun
• The buncher
• The linac itself

Each part is responsible for a stage in the acceleration of the electrons.

 

A. The Electron Gun

 

The electron gun (see electron gun theory), located at the left in the drawing, is where electron acceleration begins. The electrons start out attached to the molecules in a plate of barium aluminate or other thermionic materials such as thorium. This is the cathode of the electron gun. A cathode is a surface that has a negative electrical charge. In linac electron guns this charge is usually created by heating the cathode. Barium aluminate is a "thermionic" material; this means that it's electrons tend to break free of their atoms when heated. These electrons "boil" near the surface of the cathode.

 

The gate is like a switch. It consists of a copper screen, or "grid," and is an anode. An anode is a surface with a positive electrical charge. Every 500 millionth of a second the gate is given a strong positive charge that causes electrons to fly toward it from the cathode in tremendous numbers. As these electrons reach the gate, they become attracted even more strongly by the main anode, and pass through the gate.

 

Because the gate is pulsing at a rate of 500 million times per second (500 MHz), the electrons arrive at the anode in loose bunches, a 500 millionth of a second apart. The anode is a torus (a doughnut) shaped to create an electromagnetic field that guides most of the electrons through the hole into the next part of the accelerator, called the buncher.

 

B. The Buncher

 

The purpose of the buncher is to accelerate the pulsing electrons as they come out of the electron gun and pack them into bunches. To do this the buncher receives powerful microwave radiation from the klystron. The microwaves accelerate the electrons in somewhat the same way that ocean waves accelerate surfers on surfboards. Look at the following graph:

 

 

The yellow-orange disks are electrons in the buncher. The curve is the microwave radiation in the buncher. The electrons receive more energy from the wave--more acceleration--depending on how near they are to the crest of the wave, so the electrons riding higher on the wave catch up with the slower ones riding lower. The right-hand wave shows the same group of electrons a split second later. On the front of the wave, the two faster electrons have almost caught up with the slower electron. They won't pass it though, because they are now lower on the wave and therefore receive less acceleration.

 

The higher electron on the back of the wave gets just enough acceleration to match the speed of the wave, and is in the same position as it was on the left-hand wave. This represents the last electron in the bunch. The lower electron on the back of the wave gets too little energy to keep up with the bunch and ends up even lower on the right-hand wave. Eventually it will fall back to the electron bunch forming one wave behind.

 

C. The Linac

 

The linac itself is just an extension of the buncher. It receives additional RF power to continue accelerating the electrons and compacting them into tighter bunches. Electrons enter the linac from the buncher at a velocity of 0.6c--that's 60% of the speed of light. By the time the electrons leave the linac, they are traveling very close to the speed of light.

How does an electron gun work

---

Message:

Excellent question!

Your thoughts on the subject are correct, but the trick lies in tricking the electrons (or any other charged particle, e.g. a mass spectrometer).  What you do is build the anode with a hole in it.  This is almost certainly what they taught you, and you were completely correct in thinking that the electrons or ions would just be reattracted to the anode.  However, what they did not tell you was that immediately behind the anode was another plate with a hole in it, the holes being aligned.  This second plate is usually called the suppressor, and the key thing to making this work is that the suppressor is either grounded OR at a voltage opposite in polarity to the anode.  [Question for you:  if you're working with electrons, what polarity would you make the anode and the suppressor?]  So now the electrons coming off of the anode are accelerated and those that make it through the hole in the anode immediately pass through the hole in the suppressor as well.  This suppressor (which can be a plate with a hole in it or a grid) shields the electrons that passed through the hole from the anode and a rough beam is formed so we've sort of “tricked” the electrons.  Now, generally you want a fine (collimated) electron beam so you put a second anode/suppressor section in.  As before, not all the electrons will hit this second hole BUT those that do tend to be well collimated.  You are correct in thinking that you can do this stunt any number of times and the end result will be a high velocity, finely collimated beam of electrons which is generally steered magnetically.  The only limitations on this technique are physical size and voltage breakdown between the various plates.  But this is the method used.

 

A variant of this technique is sometimes useful when you want to get as many electrons or ions as possible and you don't care about forming a beam.  One example would be a vacuum tube.   What you do is make the anode a grid so that only a few electrons/ions strike the grid wires;  the rest pass right through.  Then you use a suppressor grid and make the final anode relatively large.  FYI, this is what high-power radio stations do to get the power (several kilowatts/tube) output required.  So as you continue your education please don't disdain vacuum tubes;  they can be very useful.

5 ELECTRON SOURCES

 

5.1 Introduction

To obtain good characteristics, the electrons, in general, need to be emitted from a well defined surface in a controlled manner. The actual design of an electron gun is mainly a function of the use of the required beam and in general is amenable to computer simulation. Only the basics of electron emission will be dealt with here; the formation of the beam is dealt with in specialist texts (e.g. [23]).

 

5.2 Thermionic Emission

Thermionic emission is the escape of electrons from a heated surface. Electrons are effectively evaporated from the material. To escape from the metal, electrons must have a component of velocity at right angles to the surface and their corresponding kinetic energy must be at least equal to the work done in passing through the surface [24]. This minimum energy is known as the 'work function'. If the heated surface forms a cathode, then at a given temperature T (° K) the maximum current density emitted is given by the Richardson/Dushman equation:-
 

J = A . T² . e ^{( -11600 .  / T )}

 

where  is the work function (eV) and A is a constant with a theoretical value of 120 A/cm².K. In reality this value is not attained for real materials. Table 3 illustrates the basic characteristics of some thermionic emitter materials that are commonly used. It can be seen that the most important parameter for thermionic emission is that the work function as should be as low as possible to use a cathode at an acceptable temperature. The mixed oxide cathode is commonly found in small radio type valves. Cs/W/O, although not good for thermal emitters, is usually found in photo-tubes whilst the heavy metal cathodes are used in high power electron tube devices.
 

Table 3 Important characteristics of some thermionic emitter materials

 

 

In a diode structure, electrons leaving the cathode surface lower the electric field at the surface. A stable condition exists when the field is zero as any further reduction would repel electrons back to the cathode. This stable regime is known as 'space-charge-limited emission' and is governed by the Child Langmuir equation:-

 

J = P . V ^3/2

 

where P, a constant which is a function of the geometry of the system, is known as the perveance. However, if the voltage becomes sufficiently high, the Richardson limit for current is reached when the emission becomes temperature limited. Figure 15 shows the characteristics of an ideal diode (top next page).

 

Fig. 15 Thermionic emission regimes

 

Thermionic emitters are used in electron tubes and in specialist electron guns, as for example in klystrons, welding, industrial materials processing and in accelerators for lepton production. Figure 16 shows a computer simulation of an electron gun used for hadron beam cooling.
 

 

Fig. 16 Computer simulation of an electron gun

 

5.3 High field emission

The application of a high voltage between a fine point cathode and a contra surface can, by a tunneling effect, give sufficient energy to an electron so that it escapes from the surface. This phenomena is known as high-field or Fowler/Nordheim emission. It should not be forgotten that the electric field around a point is greatly enhanced relative to the apparent average electric field between the electrodes. The current density (A/m²) emitted by such a point is given by :-
 

J = (1.54 . 10^-10 . E2 / ) . e ^{(-6.83*109 . 3/2 . k / E)}

 

Where E is the electric field at the emitter,  the work function and k a constant approximately equal to 1.

 

With fields of the order of 10⁹V/m, current densities can attain 10¹² A/m² but the actual current is quite small due to the small surface of the emitter. More reasonable currents can be obtained by multiplying the emitter sites. Needles or razor blades can be used as emitter arrays and arrays etched in silicon have shown some success in electron tubes. The major disadvantage of this type of source is that an excessive current density can destroy the points either by erosion or self heating.

 

5.4 Photo emission

Photons illuminating a metal surface may also liberate electrons. If the photon has an energy at least equal to the work function, then electrons will be emitted, i.e.:-  

 

< h . c / e. 

 

where  is the wavelength of the incident light, c the velocity of light and h Plank's constant. For shorter wavelengths the electrons are emitted with an initial velocity given by
 

1/2 . m . v² = h .  - e . 

 

but in general these velocities are low. To obtain reasonable emission with normal wavelengths, a low work function material is needed, for this reason the Cs/O/W material mentioned earlier is often used in photo tubes. Intense electron beams require intense light sources, and lasers have been used to obtain very short high intensity electron beam pulse trains intended for the generation of microwave power in future linear colliders.

 

IV. Vacuum Systems

A. Purpose

All of the accelerator systems rely on accelerating particles to high velocities. To allow the transfer of energy to the beam to be as efficient as possible, it is important to have no particles in the beam path which may undergo collisions with the beam and subsequent momentum transfer. This would cause a scattering of the beam, resulting in it diffusing away. Another problem which would arise in an accelerator with unevacuated beampipes would be limitations on the maximum electric field gradients attainable in the RF cavities. The high electric fields would cause an ionization of the air, forming a path to ground, reducing the electric field.

To overcome these problems, it is necessary to have evacuated regions wherever the beam is intended to travel or high field gradients would be present. These regions are enclosed in beampipe, or the magnet casing itself. Ideally the vacuum should be the best attainable, but a balance between the cost of the system verses the time beam stays in the accelerator must be reached.

 

B. Background information

When one talks about air pressure in a vessel, one is actually referring to the force on a unit area caused by the air molecules hitting the wall of the vessel. Using the Ideal gas law equation,

and solving for P,

one can see that the pressure, P, in a vessel can be reduced by increasing the volume, V, of the vessel, decreasing the temperature, T, of the gas in the vessel, or by reducing the number of particles, n, in the vessel. The most practical approach is the latter, although the reduction in temperature approach is utilized to some extent in the Tevatron.

 

1. Pressure 

The measurement of the force per unit volume is done using various instruments attached to the vacuum vessel. The typical units of pressure, one is normally used to, would be millimeters of mercury, mm Hg, with room pressure being something on the order of 760 mm Hg at sea level. In vacuum work, another set of units is used, the Torr. 760 Torr is equal to one atmosphere (760 mm Hg). A good vacuum used here at Fermilab would measure about 10^-8 - 10^-10 Torr. Below is a table of conversion between different units.

1 Atmosphere 760 mm of Hg

1 Atmosphere 14.7 psi

1 Torr 1 mm of Hg

1 Micron 10^-3 Torr

The basic component of any vacuum system is the beampipe. It is typically constructed out of stainless steel, aluminum or copper with ports welded on to provide access to the vacuum chamber.

The evacuation of a vacuum vessel, such as beampipe, is done in stages, with one type of pump removing air molecules until the pressure is reduced to where the next type of pumping will be effective. At that point one system is removed from the pumping process, and the next stage of pumping begins until the pressure is reduced to the next stage.

 

C. Components

1. Roughing pumps

The first stage of pumping is done using an oil roughing pump. This type of pumping is effective from room atmosphere to about 10^-3 Torr. The pump consists of a wheel with vanes on the perimeter lubricated with oil. As the wheel rotates, the vanes trap air molecules from the vacuum vessel between the wheel and the pump wall, and transport them to the exhaust port of the pump via a one-way valve to be expelled into the air.

2. Turbo pumps

Roughing pumps usually are helped out by Turbo pumps which can work from 10^-1 Torr to 10^-6 Torr. They work as 'turbochargers' for the roughing pumps. The turbopump consists of different layers or planes of vanes rotating at very high velocity (50,000-100,00 rpm). The pump works on the principle of momentum transfer. As the vanes spin and hit air molecules, they are driven towards the exhaust of the turbopump and into the intake of the roughing pump. Since the number of molecules at the intake of the roughing pump intake have been increased, so has the pressure - back into the efficient operating region of the roughing pump.

 

 

 

 

3. Diffusion pumps

Another system of pumping is by using oil diffusion pumps. Currently only Main Ring uses this type of pumping. They can operate in the pressure region of 10^-3 to 10^-8 Torr. The principle they operate on is the same as the turbopump - momentum transfer. In an oil diffusion pump, oil is heated to its boiling point and forced up through a tube into a number of bell shaped structures which direct the oil vapor back down toward the base of the pump and toward the exhaust of the diffusion pump. As the oil vapor is forced down, it may hit air molecules and direct them towards the exhaust of the diffusion pump, and then into the intake of a roughing pump.

 

4. Ion pumps

Ion pumps work on a different philosophy than the pumps discussed so far. Instead of aiding in moving the gas from the inside of the evacuated chamber to the outside, ion pumps keep the gas in the vacuum chamber. The ion pump consists of two titanium plates with a titanium cell structure in the middle, electrically insulated from the two plates. The cellular structure is at a potential of 5kV. There is a magnetic field set up perpendicular to the titanium plates. As a air molecule travels into the ion pump, it is ionized by the high potential, and the electron is driven towards the cellular structure, whereas the ion moves toward one of the titanium plates. Both the electron and the ion move in circular paths due to the magnetic field. This spiraling motion is done to increase the path length of the ion or electron, thereby increasing the probability that the ion or electron will hit another air molecule, ionizing it. Once the electron hits the cell structure, it may liberate a titanium ion which will be accelerated towards the titanium plates. Once the ionized air molecule hits the titanium plate, it will either react with the titanium surface, bonding with the titanium, or be trapped on the surface of the titanium plate and get covered over by some of the ionized titanium ions from the cell structure. In either case, the air molecule will no longer contribute to the pressure inside the vacuum vessel. This, of course, means that ion pumps have a finite lifetime after which their surfaces are so contaminated with oxides and such that they can no longer pump effectively. Typically this lifetime is 50,000 hours. Ion pumps are effective from 10^-5 to 10^-12. Torr

5. Sublimation pumps

Titanium sublimation pumps or 'getter' pumps work on a principle similar to the ion pump. The sublimation pump consists of rods of titanium connected to an external power supply. The idea is to evaporate some of the titanium from the rods and have it condense on nearby surfaces where it will readily interact with any air molecules that impinge on it. Again, the air molecules are then chemically trapped on the vessel wall, unable to contribute to the pressure.

 

6. Cryo-pumping

This type of pumping is more of a concept rather than a specific type of system. Anywhere a very cold object is brought in contact with a vacuum vessel there will be cryo-pumping by the simple fact that some air molecules will condense on the cold surface. As long as the surface remains cold, the air molecules will remain in a liquid state, thereby reducing the pressure in the vessel. This pumping method is used in the Tevatron where liquid helium is in close proximity to the beampipe, reducing it's walls to around 4 Kelvin. At that temperature, all gases are either liquid or solid. Another approach that is more common for the operator to encounter is the cold trap. This device is placed on the intake of an oil-based pump like a roughing pump or a diffusion pump. The cold trap is essentially a dewar or 'thermos' in contact with the evacuated space. It is filled with liquid nitrogen (77 Kelvin) and works to condense out any oil molecules that may have flowed out of the inlet of the roughing or diffusion pump.

 

7. Gauges

To measure the pressure in an evacuated vessel there are primarily three types of gauges; thermocouple gauges, cold cathode gauges, and ion gauges.

 

Thermocouple gauges work on the principle of heat convection. A heated wire is exposed to an evacuated chamber. A thermocouple is placed in thermal contact with the heated wire. As the pressure is reduced around the heated wire, the thermocouple will detect a warmer wire because there is no loss of heat from the wire due to the surrounding air molecules transporting some of the heat away. They are usable from atmospheric pressure to about 10^-3 Torr.

 

Cold cathode gauges are actually mini ion pumps. The center cell is replaced with a loop at a high potential. The amount of current that flows between the center loop and the wall of the gauge due to gas ionization is a measure of the vacuum. These gauges can operate in the range from 10^-3 to 10^-8 Torr.

 

Ion gauges work on the principle of ionization. A filament is heated liberating electrons. These electrons are accelerated towards a collector. As they travel this short path, they will ionize some of the gas molecules around the gauge. These ions are also picked up by the ion gauge. The amount of ionization is related to the pressure. Ion gauges are operable from 10^-2 to 10^-10 Torr.

 

D. Considerations in constructing a system

Gases have a tendency to attach to the surface of the metal, and slowly break away when the surface is under reduced pressure. The surfaces of some metals are porous, allowing gases to pass from one wall of the container to the other, or full of pits, providing small cavities where gases can be trapped, and then slowly bleed into the vacuum space once the surface is under reduced pressure. The process of releasing gases from the surface of a material under reduced pressure is known as outgassing. In some instances, it is desired to cause outgassing. In some instances, the outgassing is not caused by trapped gases being liberated, but by something on the surface actually evaporating into the vacuum space. This is the case with rubber or hydrocarbon-based components connected to the vacuum system. Even touching the inner surface of a vacuum vessel (the beampipe for instance) with your bare hand can leave behind body oils which can cause problems during pumpdown.

 

Outgassing is sometimes intentionally induced in vacuum components to remove these trapped gases, or ‘boil off? oils on the inner surface of vacuum vessels allowing them to be completely removed from the vacuum vessel. This is sometimes done in the Antiproton source and the Tevatron. By raising the temperature of the vacuum vessel (?baking it?) with heat blankets, any gases trapped on the inner surface of the vacuum vessel will be driven off to be pumped out by a roughing pump/turbo pump combination. Once the system has been sufficiently ‘baked', the blankets are turned off, the vacuum valves connecting the pumping station to the vessel are shut, and the ion pumps and sublimation pumps are turned on.

 

III. Accelerator Beam energy.

A. Introduction..

In any discussion of accelerators one typically discusses the 'energy' of the accelerator, or more specifically the beam energy. In this section, the concept of beam energy, its relationship to momentum and velocity will be discussed.

B. Use of relativity for velocity determination..

Since the kinetic energy particle energies are on the same order of or are above the rest energy of a proton, the methods to calculate velocities must take into account relativistic effects. A quick review of relativity will be given here to refresh the reader on the equations used.

First of all, there are a few constants that are used in the equations that will be defined here to remove any ambiguity.

 

Given the above equations, the relationship between velocity and kinetic energy can be found. Specifically, solving for beta from the last equation,

One can solve for the velocity at this point, but it is more common to express the velocity in the percentage of the speed of light that a particle is traveling. This is referred to as the Lorentz Beta..; Below is a table of some of the beam energies seen in Fermilab accelerators as well as the corresponding Lorentz beta and Lorentz gamma..